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Systematic study of particle spectra in heavy-ion collisions using Tsallis statistics

Systematic study of particle spectra in heavy-ion collisions using Tsallis statistics. Ming Shao, Zebo Tang, Yi Li, Zhangbu Xu CPPT/USTC. Introduction & Motivation Why and how to implement Tsallis statistics in Blast-Wave framework Results strange hadrons vs. light hadrons

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Systematic study of particle spectra in heavy-ion collisions using Tsallis statistics

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  1. Systematic study of particle spectra in heavy-ion collisions using Tsallis statistics Ming Shao, Zebo Tang, Yi Li, Zhangbu Xu CPPT/USTC • Introduction & Motivation • Why and how to implement Tsallis statistics in Blast-Wave framework • Results • strange hadrons vs. light hadrons • beam energy dependence • J/y radial flow • Conclusion ATHIC2010, Oct 18-20, Wuhan

  2. Thermalization and Radial flow in HI STAR whitepaper Phys. Rev. Lett. 92 (2004) 182301 Thermalization in heavy-ion collisions ? －particle ratios agree with thermal prediction Matter flows in heavy-ion collisions – all particles have the same collective velocity ATHIC2010, Oct 18-20, Wuhan

  3. Blast-wave analysis Multi-strange decouple earlier than light hadrons, with less radial flow velocity ATHIC2010, Oct 18-20, Wuhan

  4. Hydrodynamics evolution π, K, p Multi-strange W Hydro parameters: 0 = 0.6 fm/c s0 = 110 fm-3 s0/n0 = 250 Tcrit=Tchem=165 MeV Tdec=100 MeV Ulrich Heinz, arXiv:0901.4355 Multi-strange particle spectra can be well described by the same hydrodynamics parameters as light hadrons in contrast to the Blast-wave results ATHIC2010, Oct 18-20, Wuhan 4

  5. boosted E.Schnedermann, J.Sollfrank, and U.Heinz, Phys. Rev. C48, 2462(1993) random Extract thermal temperature Tfo and velocity parameter T Blast-Wave Model • Assumptions: • Local thermal equilibrium  Boltzmann distribution • Longitudinal and transverse expansions (1+2) • Temperature and T are global quantities BGBW: Boltzmann-Gibbs Blast-Wave ATHIC2010, Oct 18-20, Wuhan 5

  6. STAR PRL99 Limitation of the Blast-wave STAR PRC71 (2005) 64902 • Strong assumption on local thermal equilibrium • Arbitrary choice of pT range of the spectra • Non-zero flow velocity <bT>=0.2 in p+p • Lack of non-extensive quantities to describe the evolution from p+p to central A+A collisions • mT spectra in p+p collisions Levy function or mT power-law • mT spectra in A+A collisions Boltzmann or mT exponential AuAu@200GeV pp@200GeV minbias ATHIC2010, Oct 18-20, Wuhan 6

  7. Particle pT spectra: Exponential  Power law Non-extensive Tsallis statistics C. Tsallis, H. Stat. Phys. 52, 479 (1988) http://www.cscs.umich.edu/~crshalizi/notabene/tsallis.html http://tsallis.cat.cbpf.br/biblio.htm Wilk and Wlodarzcyk, PRL84, 2770 (2000) Wilk and Wlodarzcyk, EPJ40, 299 (2009) ATHIC2010, Oct 18-20, Wuhan

  8. Tsallis statistics in Blast-wave model BGBW: With Tsallis distribution: Tsallis Blast-wave (TBW) equation is: ATHIC2010, Oct 18-20, Wuhan

  9. Fit results in Au+Au collisions Phys. Rev. C 79, 051901 (R) (2009) ATHIC2010, Oct 18-20, Wuhan 9

  10. Fit strange hadrons only All available species Strangeness, Au+Au 0-10%: <b> = 0.464 +- 0.006 T = 0.150 +- 0.005 q = 1.000 +- 0.002 chi^2/nDof = 51/99 Tstrange>Tlight-hadrons Strangness decouple from the system earlier ATHIC2010, Oct 18-20, Wuhan 10

  11. Centrality dependence for T and <bT> • Multi-strange hadrons decouple earlier • Hadron rescattering at hadronic phase doesn’t produce a collective radial flow, instead, it drives the system off equilibrium • Partons achieve thermal equilibrium in central collisions ATHIC2010, Oct 18-20, Wuhan 11

  12. Beam energy dependence • The radial flow velocity at SPS is smaller than that at RHIC. • Freeze-out temperatures are similar at RHIC and SPS. • The non-equilibrium parameter (q-1) is small in central nucleus-nucleus collisions at RHIC and SPS except a larger (q -1) value for non-strange hadrons at RHIC energy ATHIC2010, Oct 18-20, Wuhan 12

  13. How about heavy hadrons? ATHIC2010, Oct 18-20, Wuhan 13

  14. Grandchamp, Rapp, Brown PRL 92, 212301 (2004) nucl-ex/0611020 Puzzle! Regeneration? Test with J/y flow. J/y suppression at RHIC ≈ J/y suppression at SPS (energy differs by ~10 times) J/y suppression at RHIC and SPS • quarkonium – gloden probe of QGP • deconfinement (color screening) • thermometer ATHIC2010, Oct 18-20, Wuhan 14

  15. J/y Elliptic flow J/y Heavy Flavor decay electron Alan Dion, QM2009 Too early to compare with models Won’t have enough statistics before 2011 Ermias T. Atomssa, QM2009 ATHIC2010, Oct 18-20, Wuhan 15

  16. How about radial flow? Sizeable radial flow for heavy flavor decay electrons Yifei Zhang, QM2008, STAR, arXiv:0805.0364 ATHIC2010, Oct 18-20, Wuhan 16

  17. <b> = 0.06 +- 0.03 T = 0.134 +- 0.006 q =1.0250 +- 0.0014 c2/nDof = 85.03 / 26 J/y radial flow J/y radial flow consistent with 0 Inconsistent with regeneration ATHIC2010, Oct 18-20, Wuhan 17

  18. Summary Identified particle spectra from SPS to RHIC have been analyzed with Tsallis statistics in Blast-wave description (light hadrons, multi-strange hadrons, charmonium) We found in HIC • Partonic phase • Partons achieve thermal equilibrium in central heavy-ion collisions • J/y is not thermalized and disfavors regeneration • Multi-strange hadrons decouple earlier • Hadronic phase • Hadronic rescattering doesn’t produce collective radial flow • It drives the system off equilibrium • Radial flow reflects that when the multi-strange decouples Thank you! ATHIC2010, Oct 18-20, Wuhan 18

  19. Back up ATHIC2010, Oct 18-20, Wuhan 19

  20. Check— Parameter Correlation <b> = 0.0954 +- 0.0828 T = 0.1777 +- 0.0328 q = 1.0106 +- 0.0022 c2/nDof = 151.53 / 37 <b> = 0.0000 +- 0.0000 T = 0.1747 +- 0.1644 q = 1.0708 +- 0.0435 c2/nDof = 12.83 / 13 ATHIC2010, Oct 18-20, Wuhan 20

  21. Check—Strangeness and light hadrons ATHIC2010, Oct 18-20, Wuhan 21

  22. Results in p+p collisions ATHIC2010, Oct 18-20, Wuhan 22

  23. Temperature fluctuation Reverse legend Wilk and Wlodarzcyk, EPJ40, 299 (2009) Wilk and Wlodarzcyk, PRL84, 2770 (2000) ATHIC2010, Oct 18-20, Wuhan 23

  24. PHENIX Beam Use Request ATHIC2010, Oct 18-20, Wuhan

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